How do I parent a mesh, transferring the vertex groups?
OK, I stumbled upon the answer. Perhaps settings have changed since the 2.6x series but I found that for Transfer Weights, settings appear underneath with one of them referring to "Source Layer".  Setting this to "All Layers" when doing the Transfer Weights causes all the weights AND vertex groups to transfer to the new mesh.  After that, just delete the original mesh and then parent the new mesh to the armature.